Answer: 33
<u>Step-by-step explanation:</u>
The ratio of Adhy's to Ben's is 3:4 so let
Adhy = 3x
Ben = 4x
Since Ben = Adhy + 9
then 4x = 3x + 9
--> x = 9
So, Adhy = 3x = 3(9) = 27
Ben = 4x = 4(9) = 36
*************************************************************
The ratio of Ben's to Clayson's is 3:5
How do we get Ben's ratio of 3 equal to 36? <em>by multiplying by 12</em>
Ben : Clayson
<u>3 x 12</u> <u>5 x 12</u>
36 60
So, Clayson = 60
***********************************************************
The difference between Adhy and Clayson is:
Clayson - Adhy
60 - 27 = 33
Answer:
see explanation
Step-by-step explanation:
Using the sum/ difference → product formula
cos x - cos y = - 2sin(
)sin (
)
sin x - sin y = 2cos (
)sin (
)
Given
(cosA - cosB)² + (sinA - sinB )²
= [ - 2sin(
)sin(
) ]² + [ 2cos(
)sin(
) ]²
= 4sin² (
)sin² (
) + 4cos² (
)sin² (
)
= 4sin² (
)[ sin² (
) + cos² (
) ← sin²x + cos²x = 1
= 4sin² (
) × 1
= 4sin² (
) = right side ⇒ proven
Answer:
15) a) 8
b) y + 2
c) y - 1
16) True
17) 2n - 1, where n is an integer
18) a) 3p + 4q
b) 500 - 3p - 4q
Answer:
<em>x = 2</em>
Step-by-step explanation:
<u>Exponential Equations</u>
Solve:

Separate each exponential:

Operating:

Multiplying by 5:

Rearranging:

Recall that:


Calling


Factoring:

There are two possible solutions:
y=25
y=-50
Since

y cannot be negative, thus:

The solution is:
x = 2